QQuestion
If x = 4√15 \over √5 + √3, then find the value of x + √20 \over x − √20 + x + √12\over x - √12
✓Answer
x = 4√15 \over √5 + √3
⇒ x = √240 \over √5 + √3
⇒ x = √12 × √20 \over √5 + √3
⇒ x\over √20 = √12 \over √5 + √3
⇒ x + √20\over x - √20 = 2√3 + √5 + √3\over 2√3 - √5 - √3
⇒ x + √20\over x - √20 = 3√3 + √5\over √3 - √5 —- (i)
Again, x\over √12 = √20 \over √5 + √3
⇒ x + √12\over x - √12 = 2√5 + √5 + √3\over 2√5 - √5 - √3
⇒ x + √12\over x - √12 = 3√5 + √3\over √5 - √3 —- (ii)
Adding (i) and (ii)
⇒ x + √20\over x - √20 + x + √12\over x - √12 = 3√3 + √5\over √3 - √5 – 3√5 + √3\over √3 - √5
⇒ x + √20\over x - √20 + x + √12\over x - √12 = 3√5 + √3 - 3√5 - √3\over √3 - √5
⇒ x + √20\over x - √20 + x + √12\over x - √12 = 2(√3 - √5)\over √3 - √5 = 2
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